Automatic Control of a 3 MWe SEGS VI Parabolic Trough Plant Thorsten Nathan Blair John W. Mitchell William A. Becman Solar Energy Laboratory University of Wisconsin-Madison 15 Engineering Drive USA E-mail: becman@engr.wisc.edu Abstract For the 3 MWe SEGS VI Parabolic Trough Collector Plant one tas of a silled plant operator is to maintain a specified point of the collector outlet temperature by adjusting the volume flow rate of the heat transfer fluid circulating through the collectors. For the development of next generation SEGS plants and in order to obtain a control algorithm that approximates an operator s behaviour a linear model predictive controller is developed for use in a plant model. The plant model is discussed first in this wor. The performance of the controller is evaluated for a summer and a winter day. The influence of the control on the gross output of the plant is examined as well. 1. INTRODUCTION A solar electric generating system (SEGS) shown in Figure 1 refers to a class of solar energy systems that use parabolic troughs in order to produce electricity from sunlight (Pilington 1996). The parabolic troughs are long parallel rows of curved glass mirrors focusing the sun s energy on an absorber pipe located along its focal line. These collectors trac the sun by rotating around a north-south axis. The heat transfer fluid () an oil is circulated through the pipes. Under normal operation the heated leaves the collectors with a specified collector outlet temperature and is pumped to a central power plant area. There the is passed through several heat exchangers where its energy is transferred to the power plant s woring fluid which is water or steam. The heated steam is used in turn to drive a turbine generator to produce electricity. The facility discussed in this paper is the 3 MWe SEGS VI plant constructed in 1988 by Luz International Ltd. and is located in the Mojave desert of southern California. A silled operator controls the parabolic trough collector outlet temperature. One of his tass is to maintain a specified point for the collector outlet temperature by adjusting the volume flow rate of the within upper and lower bounds. The collector outlet temperature is mainly affected by changes in the sun intensity by the collector inlet temperature and by the volume flow rate of the. The ambient temperature and the wind speed also influence the outlet temperature but their influence is small. Knowledge of the sun s daily path observation of clouds and many years of experience and training give the operator the ability to accomplish his tas. But there are limitations on the performance of a human controller. Thus for the development of next generation SEGS plants it is reasonable to loo at automatic controls. In addition a control algorithm that approximates an operator s behavior can be included in simulation models of SEGS plants. Automatic control of the in a parabolic trough collector through proportional control has been previously addressed (Schindwolf 198). In this study a linear model predictive controller is developed for the SEGS VI plant. The essential idea behind model predictive control (MPC) is to optimize forecasts of process behavior. The forecasting is accomplished with a process model. Therefore the model is the essential element of a MPC controller (Rawlings 2). The control strategy considers constraints on both the collector outlet temperature and the volume flow rate of the. The control performance is evaluated through simulations. Consequently it is very important to obtain an accurate model of the plant on which the controller can be tested. The following section deals with the modeling of the plant. The control issue is discussed in a later section.
Solar Collector Field HP- LP- ~ Generator Pump Expansion Vessel Reheater Preheater Steam Generator Deaerator Condenser Condensate Pump Superheater HP- Feedwater Heater Feedwater Pump LP- Feedwater Heater Figure 1 Flow Diagram of the 3 MWe SEGS VI Plant for Pure Solar Mode 2. THE PLANT MODEL In the following the plant is divided into two subsystems: the solar collector field and the power plant. Both are shown schematically in Figure 1. 2.1. The Solar Collector Field The thermal performance model of the SEGS VI parabolic trough plant is based upon a steady-state efficiency model for the collector using empirical coefficients (Lippe 1995). These coefficients were obtained experimentally on a test facility at SANDIA. Glass Envelope Absorber Tube Heat Transfer Fluid Partial Vacuum between Envelope and Absorber Figure 2 The Heat Collection Element ISES 21 Solar World Congress 2
A detailed physical model for the collector is presented in this wor. To derive the appropriate differential equations the heat collection element (HCE) in Figure 2 is considered. The HCE consists of the absorber pipe in which the flows. A glass envelope covers the absorber pipe which is assumed to have no radial temperature gradients. Partial vacuum exists in the annulus between the absorber pipe and the glass envelope. A Transient energy balance for the leads to the following partial differential equation for the temperature: T T ρc AABS i = ρc V ( t) + π DABS ihabs ( TABS T ) (1) t z with ρ c T as the density specific heat and temperature. The cross-sectional area of the inside tube of the absorber is A ABS i and the inside diameter of the absorber tube is D ABS i. The heat transfer coefficient determining the heat transmitted between the absorber and the is h. The volume flow rate is ABS V. Note that the delay time varies from approximately 3 minutes at the minimum flow rate to.5 hour at the maximum flow rate. The distance along the collector is z and t is the time. The boundary condition for equation (1) is T ( t) = T inlet ( t) (2) with T as the collector field inlet temperature. The initial condition for equation (1) is inlet T z = T. (3) ( ) The differential equation for the absorber temperature is given through TABS ρ ABS c ABS AABS = Qabsorbed Qinternal π D ABS i habs ( TABS T ) (4) t with ρ c T as the absorber density specific heat and temperature. The cross-sectional area of the ABS ABS ABS absorber is A ABS. The absorbed solar energy is Q absorbed and Q internal is the heat transfer between the absorber and the envelope. The initial condition for equation (4) is T z = T. (5) ABS ( ) ABS The glass envelope is assumed to have no radial temperature gradients. The differential equation for the envelope temperature is given through TENV ρ ENV cenv AENV = Qinternal Qexternal (6) t with ρ ENV c ENV TENV as the envelope density specific heat and temperature. The heat transfer between the envelope and the environment is Q external. The initial condition for equation (6) is T z = T. (7) ENV ( ) ENV The heat transfer coefficient h ABS is calculated through the Dittus-Boelter equation for turbulent flow in circular tubes. The heat transmitted between the absorber and the envelope Q internal is calculated from free convection flow in the annular space between long horizontal concentric cylinders and radiation. The heat transfer between the envelope and the environment Q external is estimated through relations for a circular cylinder in cross flow and radiation. The absorbed solar energy Q absorbed is the direct normal solar radiation that is absorbed by the absorber after accounting for optical losses. Because of the north-south tracing of the collectors only the direct normal solar radiation times the cosine of the angle of incidence is available as heat energy (Duffie & Becman 1991). This ISES 21 Solar World Congress 3
energy is further reduced through mirror reflectivity dirt on the mirrors transmissivity of the envelope absorptivity of the absorber the mutual shading of the collectors during the sun rise and the sun end losses and additional losses due to shading by the HCE arms and bellows. The parameters to calculate these losses were taen from an experimentally verified steady-state model developed at SANDIA (Mancini et al. 21). The solar collector field model predicts the solar collector field outlet temperature well especially for days with good weather conditions. Figure 3 shows the predicted and measured solar collector field outlet temperature for December 14 1998 which was a cloudy day. Even for a day with bad weather conditions the predicted temperature matches the measurement sufficiently. 7 Collector Outlet Temperature 65 6 T out [K] 55 5 45 4 35 3 Figure 3 Collector Outlet Temperature of the Solar Collector Field for December 14 1998. The solid line represents the Outlet Temperature calculated through the Solar Collector Field Model whereas the dashed line represents measured Data. 2.2. The Power Plant The power plant as seen in Figure 1 is a Ranine cycle with reheat and feedwater heating. For simplicity each heat exchanger networ consisting of preheater (economizer) steam generator (boiler) and superheater is treated as a single heat exchanger in the model. In the same manner the two high-pressure feedwater heaters are modeled as one high-pressure feedwater heater and the three low-pressure feedwater heaters are modeled as one single low-pressure feedwater heater. The power plant model is a steady-state model. The effectiveness and the heat transfer coefficients in the heat exchangers are functions of the steam / water mass flow rate. The pump and turbine efficiencies are assumed to be constant with values taen from (Lippe 1995). 3. LINEAR MODEL PREDICTIVE CONTROL For the following discussion of the linear model predictive control concept it is useful to thin of the plant model as a bloc with inputs and outputs as it is shown in Figure 4. The plant model inputs not used for control are the cooling water inlet temperature at the condenser the steam or water mass flow rate in the power plant m Steam and environmental data as the solar radiation S the ambient temperature T amb and the wind speed v Wind. The input that is used to control the collector outlet temperature T out is the volume flow rate V. The MPC controller measures the collector outlet temperature and calculates the volume flow rate which is then injected into the plant model. The environmental data the steam mass flow rate and the heat exchanger water inlet temperature T Water are treated as measured disturbances and are nown by the controller as well. ISES 21 Solar World Congress 4
S Solar Radiation Ambient Temperature T amb Wind Speed v Wind d MPC Controller Collector Model Collector Outlet Temperature T out Regulator V Plant Model T out V Volume Flow Rate Steam Mass m Steam Flow Rate Cooling Water Inlet Temperature T Water Plant Model T Power Plant Model Heat Exchanger Water Inlet Te mperature Valve Adjustments Gross Output Set Points T out V T T update V update Tˆ Target Calculation ˆ T ˆ Estimator T dist T T out V Figure 4 Bloc Diagram with Plant Model and Controller Figure 5 MPC Controller States of the collector model T are given through the differential equations (1) (4) and (6). Discretization in the z direction transforms the partial differential equations into a of nonlinear ordinary differential equations with initial conditions dt dt The outlet temperature measurement is given by ( T ) + q( S T v ) = H V (8) amb Wind T ( ) = T. (9) ( T ) T out = h. (1) The of ODEs given by equation (8) is linearized and transformed into a time discrete form T = AT + BV + 1 + Gd d (11) at time. An additional linear differential equation for the collector inlet temperature with respect to the collector outlet temperature the steam mass flow rate and the heat exchanger water inlet temperature was added to equation (11). Hence the disturbance vector d is of the form d S T = v m T amb Wind Steam Water. (12) The initial condition for equation (11) is T and the measurement is T = CT. (13) out ISES 21 Solar World Congress 5
Set points for the plant model are defined for the collector outlet temperature T out for the volume flow rate as the input V and for the states T. For the linearized model these points become T out V and T. A structure of a MPC controller is shown in Figure 5 (Rawlings 2). It consists of the receding horizon regulator the state estimator and the target calculation. 3.1. Receding Horizon Regulator The receding horizon regulator is based on the minimization of the following objective function at time (Rawlings 1993). min V N j= 2 2 ( Q ( T T ) + S V ) out + j out + j (14) where Q is a penalty parameter on the difference between the actual collector outlet temperature and the point temperature. The parameter S is a penalty parameter on the rate of change of the volume flow rate as the input in which V + j = V + j V + j 1. Penalizing the rate of change of the input can be useful for a better attenuation of possible oscillations which might occur in the controlled collector outlet temperature. N The vector V N contains N future optimal open-loop control moves where the first input value in V V is injected into the power plant model. In addition constraints on the collector outlet temperature on the volume flow rate and on the rate of change of the volume flow rate can be considered. 3.2. State Estimator The state estimator is a linear observer that estimates the states of the system from the input (the volume flow rate) the measured disturbances (environmental data steam mass flow rate heat exchanger water inlet temperature) and the measurement of the collector outlet temperature. Ideally the linear model should predict the same states as the actual process (in this case the non-linear detailed plant model). The differences between the collector outlet temperatures as predicted by the linear model and the detailed model are multiplied by an observer gain and fed bac to the linear model to minimize the difference. The observer gain is calculated as the discrete steady-state Kalman filter gain with the intention to minimize the mean-square error of the state estimate. The regulator with the estimator described above would not be able to control the collector outlet temperature to the point without exhibiting an off. That s why integral action in the controller is very often desirable. As part of the integral action implementation it is assumed that the difference between the collector outlet temperature prediction of the estimator and the measurement is caused by an input step disturbance which in turn is estimated as well. In some cases integral action in the control can decrease stability due to increasing differences in the dynamic between the linear model used in the controller and the nonlinear plant model on which the controller acts. 3.3. Target Calculation For off-free control the point used in the receding horizon regulator has to be updated with respect to the measured disturbance and the estimated difference between the collector outlet temperature prediction and the measurement. The latter represents the second part of the integral action implementation. The target calculation is formulated as a mathematical program to determine the new point. ISES 21 Solar World Congress 6
Tout [K] 7 65 6 55 5 45 4 35 Collector Outlet Temperature 3 V dot [m^3/s] 1.9.8.7.6.5.4.3.2.1 Volume Flow Rate Figure 6 Collector Outlet Temperature and Volume Flow Rate for June 2 1998. The Collector Outlet Temperature is simulated. For the Volume Flow Rate the dashed line represents the measured input for a human controller on that day and the solid line represents the input generated through automatic control. 7 Collector Outlet Temperature 1 Volume Flow Rate T out [K] 65 6 55 5 45 4 35 3 Figure 7 Collector Outlet Temperature and Volume Flow Rate for December 16 1998. The Collector Outlet Temperature is simulated. For the Volume Flow Rate the dashed line represents the measured input for a human controller on that day and the solid line represents the input generated through automatic control. 12 Gross Output V dot [m^3/s].9.8.7.6.5.4.3.2.1 7 Gross Output 1 6 P Gross [MW] 8 6 4 2 P Gross [MW] 5 4 3 2 1 Figure 8 Gross Output calculated through the Power Plant Model. The left figure shows the Gross Output for June 2 1998 and the right figure shows the Gross Output for December 16 1998. The smalldashed line represents the Gross Output with human control. The solid line represents the Gross Output with automatic control. The long-dashed line shows the useful energy (see text) ISES 21 Solar World Congress 7
3.4. Results The performance of the controller is shown in Figures 6 7 and 8. Two different days are considered. Figure 6 shows the collector outlet temperature and the volume flow rate for June 2 1998. For the volume flow rate the dashed line represents the adjustment made by a human controller on that day. The related collector outlet temperature calculated through simulation with the discussed plant model is the dashed line in the left figure. The volume flow rate shown as solid line represents the input calculated through model predictive control. The solid line in the left figure is the corresponding collector outlet temperature. The automatic controller is turned on at 8. hr in the morning and turned off at 18.8 hr. The start up and shut down is assumed to be done by a human. The automatic controller obtains the ability to hold the collector outlet temperature at a constant point (653.9 K) for a long time throughout the day. Its performance is better than the performance of the human controller. The occurrence of oscillations when starting the automatic control and before this controller is turned off are due to increasing differences between the linear model used in the controller and the nonlinear model as the controlled plant when reaching the transient. In Figure 7 the collector outlet temperature and the volume flow rate are shown for December 16 1998. Again dashed lines represent human control and solid lines represent automatic control. During winter days when the energy in the system is relatively low the model behavior tends to become more nonlinear. That s why integral action is excluded on that day in the automatic controller. The linear model used to control on a winter day is different from the linear model used for the control on a summer day. The automatic controller is turned on at 9: hr and turned off at 16: hr. Although a small off between the automatically controlled collector outlet temperature and the point (597.3 K) can be seen the automatic control action results in a collector outlet temperature much closer to the point compared to the human controlled one. The left hand figure in Figure 8 shows the calculated gross output for June 2 1998. The small-dashed line represents the gross output for human control. The solid line represents the gross output for automatic control. As can be seen from the two plots the fact that the automatic controller shows a better performance than the human controller in generating a constant point collector outlet temperature does not improve the gross output remarably. As an illustration of efficiency the useful energy is plotted in the graph as well. The right hand figure in Figure 8 shows the calculated gross output for December 16 1998. Also in this case there is no remarable improvement in the gross output through automatic control. 4. CONCLUSIONS A nonlinear model of the 3 MWe SEGS VI parabolic trough plant has been established. The model consists of a dynamic model for the collector field and a steady-state model for the power plant. It was used to examine the linear model predictive control strategy for maintaining a specified constant collector outlet temperature on a summer day and a winter day when the power plant was operating in pure solar mode. The implemented MPC controller showed the capability to hold the collector outlet temperature close around the specified point for a long time during a day. The automatic controller demonstrated a better control of the collector outlet temperature than the human control. However the improvement in the predicted gross output of the power plant due to the better control of the collector outlet temperature is small. Further studies should include the model predictive control strategy with the objective to maximize the gross output. Controlling both the volume flow rate and the steam mass flow rate in the power plant could help improving the daily gross output of the parabolic trough plant. 5. ACKNOWLEDGEMENTS Sandia National Laboratories is a multi-program laboratory operated by Sandia Corporation a Locheed Martin Company for the United States Department of Energy under Contract DE-AC4-94AL85. The assistance of Scott Jones of Sandia National Laboratory is greatly appreciated. ISES 21 Solar World Congress 8
6. REFERENCES Duffie J.A and Becman W.A. (1991) Solar Engineering of Thermal Process John Wiley & Sons Inc. New Yor. Rawlings J.B. and Muse K.R. (1993) Model Predictive Control with Linear Models AIChE Journal 39 (2) 262-287. Rawlings J.B. (2) Tutorial Overview of Model Predictive Control IEEE Control Systems Magazine 38-52. Lippe F. (1995) Simulation of the part-load behavior of a 3 MWe SEGS plant SAND95-1293 Sandia National Laboratories Albuquerque NM. Pilington (1996) Status Report on Solar Thermal Power Plants Pilington Solar International GmbH Cologne Germany. Mancini T. Sloan M. Kearney D. Appel F. Mahoney K. Cordeiro P. (21) LUZ Heat Collection Element Heat Transfer Analysis Model Sandia National Laboratory ISES 21 Solar World Congress 9